Quasi-local first law of black-hole dynamics

TL;DR

This paper derives a dynamical version of the first law of black hole mechanics without assuming symmetry or asymptotic conditions, introducing a new definition of dynamical surface gravity.

Contribution

It presents a novel derivation of the first law of black hole dynamics applicable to non-stationary cases, including a new definition of dynamical surface gravity.

Findings

Derived a general form of the first law for dynamical black holes

Proposed a new definition of dynamical surface gravity

Reduced to known definitions in spherical symmetry

Abstract

A property well known as the first law of black hole is a relation among infinitesimal variations of parameters of stationary black holes. We consider a dynamical version of the first law, which may be called the first law of black hole dynamics. The first law of black hole dynamics is derived without assuming any symmetry or any asymptotic conditions. In the derivation, a definition of dynamical surface gravity is proposed. In spherical symmetry it reduces to that defined recently by one of the authors (SAH).